Spin Conduction in Anisotropic 3-D Topological Insulators

When topological insulators possess rotational symmetry their spin lifetime is tied to the scattering time. We show that in anisotropic TIs this tie can be broken and the spin lifetime can be very large. Two different mechanisms can obtain spin conduction over long distances. The first is tuning the Hamiltonian to conserve a spin operator $\cos \phi \, \sigma_x + \sin \phi \, \sigma_y$, while the second is tuning the Fermi energy to be near a local extremum of the energy dispersion. Both mechanisms can produce persistent spin helices. We report spin lifetimes and spin diffusion equations.